Question

2+8+14+---------- n terms =3n^2-n prove by induction​

Answer 1

Step-by-step explanation:

let p(m) be the given statement where m is any natural number.

then,clearly p(1) is true as

p(1):

3(1)²-1

=>2

let us assume that p(k) is true where k is a natural number.i.e,

2+8+14+...+(2+(k-1)6)=3k²-k

now by induction,p(k+1) should also be true and 2+6k is the next term..

p(k+8):

2+8+14+..+(2+(k-1)6)+(2+6k)=3(k+1)²-(k+1)

LHS:

3k²-k+(2+6k)

3k²+6k+3 -k-1

3(k+1)²-(k+1)

which is RHS .....

thus,p(m) is true for all m where m is a natural number..

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